There is known, from French patent application number 2 699 749A, a brush case made by bending a metal blank defining a housing for guiding a brush in a sliding manner, and comprising cooling fins extending to the top of the case. The fins are shaped and disposed to have a large contact surface with the case and to offer a large exchange surface by convection with the ambient air. However, this case has the drawback that the bending of the blank for the manufacture of the case is complicated to perform. Moreover, the possibilities for shaping and arranging the fins remain limited and do not enable good cooling performances to be obtained.
One object of the invention is to provide a case which is easier to manufacture and which offers more possibilities and at least one cooling fin, arranged with improved cooling performance.